-3x(2x-1)=5x-30

Solution for -3x(2x-1)=5x-30 equation:

Simplifying
-3x(2x + -1) = 5x + -30

Reorder the terms:
-3x(-1 + 2x) = 5x + -30
(-1 * -3x + 2x * -3x) = 5x + -30
(3x + -6x2) = 5x + -30

Reorder the terms:
3x + -6x2 = -30 + 5x

Solving
3x + -6x2 = -30 + 5x

Solving for variable 'x'.

Reorder the terms:
30 + 3x + -5x + -6x2 = -30 + 5x + 30 + -5x

Combine like terms: 3x + -5x = -2x
30 + -2x + -6x2 = -30 + 5x + 30 + -5x

Reorder the terms:
30 + -2x + -6x2 = -30 + 30 + 5x + -5x

Combine like terms: -30 + 30 = 0
30 + -2x + -6x2 = 0 + 5x + -5x
30 + -2x + -6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
30 + -2x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -1x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + -1x + -3x2)' equal to zero and attempt to solve:

Simplifying
15 + -1x + -3x2 = 0

Solving
15 + -1x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-5 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 0.3333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 0.3333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 0.3333333333x + x2 = 0 + 5
0.3333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
0.3333333333x + x2 = 5

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 5 + 0.02777777779

Combine like terms: 5 + 0.02777777779 = 5.02777777779
0.02777777779 + 0.3333333333x + x2 = 5.02777777779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 5.02777777779

Calculate the square root of the right side: 2.242270675

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 2.242270675 and -2.242270675.

Subproblem 1
x + 0.1666666667 = 2.242270675

Simplifying
x + 0.1666666667 = 2.242270675

Reorder the terms:
0.1666666667 + x = 2.242270675

Solving
0.1666666667 + x = 2.242270675

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 2.242270675 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 2.242270675 + -0.1666666667
x = 2.242270675 + -0.1666666667

Combine like terms: 2.242270675 + -0.1666666667 = 2.0756040083
x = 2.0756040083

Simplifying
x = 2.0756040083

Subproblem 2
x + 0.1666666667 = -2.242270675

Simplifying
x + 0.1666666667 = -2.242270675

Reorder the terms:
0.1666666667 + x = -2.242270675

Solving
0.1666666667 + x = -2.242270675

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -2.242270675 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -2.242270675 + -0.1666666667
x = -2.242270675 + -0.1666666667

Combine like terms: -2.242270675 + -0.1666666667 = -2.4089373417
x = -2.4089373417

Simplifying
x = -2.4089373417

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0756040083, -2.4089373417}
Solution
x = {2.0756040083, -2.4089373417}